Criticality of the net-baryon number probability distribution at finite density

We compute the probability distribution P(N)P(N) of the net-baryon number at finite temperature and quark-chemical potential, μ  , at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For μ/T<1μ/T<1, the model exhibits the chiral crossover transition which belongs to the universality class of the O(4)O(4) spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, P(N)P(N). By considering ratios of P(N)P(N) to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to O(4)O(4) criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine O(4)O(4) criticality in the context of binomial and negative-binomial distributions for the net proton number.